Question

Drag numbers in the box to make each comparison true

Answer 1

$12\times\frac{4}{8}\lt8,\:12\times\frac{4}{6}=8,\:12\times\frac{4}{3}\gt8$

1) Let's find the results of each inequality/equality so that we write out the right choices.

2) Let's begin with the equation. We're going to resort to Algebra:

$\begin{gathered} 12\times\frac{4}{x}=8 \\ 12\times4=8x \\ 48=8x \\ 8x=48 \\ \frac{8x}{8}=\frac{48}{8} \\ x=6 \\ 12\times\frac{4}{6}=8{\color{DarkBlue} } \end{gathered}$

Based on that, we can tell that and filling in the gap with other whole numbers the following:

$\begin{gathered} 12\times\frac{4}{8}<8 \\ 6<8 \\ 12\times\frac{4}{6}=8 \\ 12\times\frac{4}{3}>8 \\ 16>8 \end{gathered}$

Note that we picked whole numbers and it is clear that the greater the denominator the lesser the value.